June 12, 2010

Review of "Bursts"

If
you recollect your daily routine, what adjective would you use to describe it?
What did you do today and in what order did you do these things? You probably
engaged in an automatic routine, with many events being the same and some of
those events occurring at roughly the same time from day to day. You also
probably do things at the same time as your neighbor. Part of this is based on the
way society is organized. Indeed, people tend to have similar schedules or
engage in the same essential activities. But an alternative hypothesis suggests
that statistical laws govern aggregate human (and natural) behavior. When
processes such as travel across human transportation networks or e-mail
correspondences unfold over time, they do so in a statistically distinct
manner. In his previous book “Linked”, Barabasi got ahead of the social
networking curve to demonstrate the power of connectedness to a general
audience. Yet connectivity has two components: the static topology, and the
dynamic, less-understood process of connection. In "Bursts", the
argument is made that dynamic behavioral patterns (such as connecting to a network)
can be characterized using a series of non-uniform statistical distributions.
These models reveal that traffic jams, long check-out lines, and even crime
waves are indeed not unpredictable events, but rather can be understood as
"bursts" that occur at relatively infrequent intervals. Yet the very
nature of their burstiness (in that they involve synchronized, collective
behavior) makes them predictable.

Your
daily schedule might involve brushing your teeth at a different time than your
neighbor, but going to work at the same time. This is one kind of behavioral
burst that is featured in Barabasi’s book. But we can also think of bursts as
excitable events that occur against either a random background. We are all
familiar with the excitability exhibited by exploding fireworks, popping
popcorn, or even neurons firing an action potential. All of these events have
one thing in common: nonlinear behavior governed by a threshold. In the case of
both popcorn and neurons, a constant stimulus is applied that eventually
triggers a change in state. In the case of both popcorn and neurons, these
bursts only become useful in the context of collective behavior (one is
immensely enjoyable, the other essential to your survival). Physicists
sometimes refer to this type of response as a first-order phase transition. In
the classic sandpile model of Bak, Tang, and Weisenfeld, the gradual growth of a sandpile
is sometime punctuated by large-scale displacements in the structure of the
sandpile. These large-scale displacements occur at low frequencies relative to
the more uniform small-scale displacements. In many cases, the distribution of
these events over time can be scaled to a power law (or 1/f) distribution,
meaning that they are fundamentally distinct from a uniform diffusive process resulting in a Gaussian distribution of events. Any good book in statistical physics can put
the significance of 1/f processes in context in addition to providing a wealth
of specific examples in nature. But how do these well-characterize physical
processes map to and help explain human behavioral bursts?

An Underlying Mechanism

One
undercurrent of this book is that excitable events, synchronized, collective
behavioral processes, and power law behavior are all part of the same subject.
This subject is the manner in which bursts unfold, which is according to a
Poisson process. While excitable events, collective behavioral processes, and
power law behavior all set the stage for bursty events, it is the Poisson
process that distributes these events stochastically with respect to time. In addition, power law behavior should be expected of a Poisson process that can be observed at all timescales. The
investigation of e-mail archives demonstrates this: most e-mail arrives at
specific times of day or on specific days of the week, with smaller clusters or
singleton events occurring in the interim. The difference between e-mail
archives and physical avalanches, however, is instructive. In the case of the
former (e-mail), the "bursts" are due to large-scale events driven by
intention. In the case of the latter (physical avalanche), the
"bursts" are due to large-scale events driven by a buildup of forces
that exceeds a threshold. In both cases, linear inputs act collectively to
produce a nonlinear output. One could argue that the "flash crash" of May, 2010 was caused by the bursty nature of the stock market, a system that
phase-space-wise resides in between the collective intention of e-mail
communication and the pure stochasticity of physical avalanches.

Barabasi
writes "Bursts" as a hybrid historical/scientific narrative: he
switches back and forth between medival Hungarian history and contemporary
scientific stories as to how bursts can be discovered in the data we all
produce. By the data we all produce, I mean that his examples focus on social
phenomena such as e-mail transactions and human mobility patterns. Besides his
own work, the book also features the work of Dirk Brockmann, a physicist who
did an experiment tracking the movement of dollar bills around the United States.
The outcome was that dollar bills diffuse according to a Levy process, or a 1/f
form of diffusion. In a Levy flight, which has also been observed for albatross
foraging behaviors, short and randomly oriented trips are punctuated by rare,
long-distance trips. As with e-mail communications, these bursts are driven in
part by intention. It is only when these intentions are joined to chance events
and then placed into the context of a process that unfolds over time that the
burstiness of behavior becomes apparent.

Conclusion

But
what can be learned from the sojourns into history? There is a strong
undercurrent of historical contingency in the stories Barabasi selects.
Intentional or not, the point is made as to the "burstiness" of how
history unfolds. Historical contingency, which refers to the dependence of
current events on the trajectory of past events, is not a purely a
deterministic process. While the path history takes is constrained by past
events, those defining events occur in a background of chance events. Often
when people tell stories about how they got a particular job or how they met a
spouse, it often involves the phrase "as luck would have it". But
perhaps bursts, made manifest by dating websites, commuter trains, and scheduling
constraints, are more responsible for these chance events than has
traditionally been recognized.